A limit theorem for the sum of squared differences of an integrated Ito process with application to inverse scattering

TL;DR

This paper proves a limit theorem for the sum of squared differences of integrated Ito processes, showing convergence to a fraction of the quadratic variation, with applications to inverse scattering on fractal surfaces.

Contribution

It establishes a new limit theorem for integrated Ito processes and applies it to inverse scattering problems involving fractal surfaces.

Findings

Sum of squared differences converges to two-thirds of the quadratic variation.

The limit theorem holds in probability for the specified functional.

Application demonstrated in inverse scattering from a fractal surface.

Abstract

We investigate a functional obtained by summing the squared differences of the integral of an Ito process over disjoint intervals. The limit of this sum is shown to converge in probability to two thirds the quadratic variation of the underlying process. An application to inverse scattering from a random fractal surface is presented.